A note on Lamarle formula in Minkowski $3$-space

Authors

  • Ufuk Öztürk Çankırı Karatekin University
  • Kazım İlarslan Kırıkkale University
  • Esra Betül Koç Öztürk
  • Emilija Nesovic University of Kragujevac

DOI:

https://doi.org/10.5556/j.tkjm.49.2018.2653

Keywords:

Pseudo-Null Curve, Ruled surface, Minkowski 3-space

Abstract

The Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field in Minkowski $3$-space. We also obtain the corresponding striction line and distribution parameter of such surface. We prove that there is no Lamarle formula when the director vector field is spacelike and its derivative is null, because the ruled surface in that case is a lightlike plane. Finally, we give some examples.

Author Biographies

Ufuk Öztürk, Çankırı Karatekin University

Department of Mathematics, Faculty of Science, University of Çankırı Karatekin, 18100 Çankırı, Turkey.

Kazım İlarslan, Kırıkkale University

Department of Mathematics, Faculty of Sciences and Art, University of Kırıkkale, 71450 Kırıkkale, Turkey.

Esra Betül Koç Öztürk

A.H.R.Mah. Çayyolu Cad. Ada Sitesi B blok No:18/12, 18100 Çankırı, Turkey.

Emilija Nesovic, University of Kragujevac

Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia.

References

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Published

2018-12-25

How to Cite

Öztürk, U., İlarslan, K., Koç Öztürk, E. B., & Nesovic, E. (2018). A note on Lamarle formula in Minkowski $3$-space. Tamkang Journal of Mathematics, 49(4), 291-300. https://doi.org/10.5556/j.tkjm.49.2018.2653

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